At least two types of radiography exist, namely, projection radiography and tomographic radiography. The term "radiography"generically refers to the use of "radiation" to produce a "graph,"or picture, of an object.
In projection radiography, such as that which produces a common X-ray photograph, an object is immersed in a beam of radiation. The radiation passes through the object, and onto photographic film, or other detector. Since the object, in general, is non-uniform in density, the different rays of radiation, within the beam, will be attenuated differently as they pass through the object.
The rays which are attenuated a small amount produce bright spots on the film. The rays which are attenuated a large amount produce dark spots on the film. (Of course, an opposite type of photographic film can be used, wherein bright spots correspond to large attenuation, and dark spots correspond to small attenuation.)
The collection of bright and dark spots on the film forms an image. Each spot indicates the overall density of the path, through the object, taken by its respective ray.
In tomographic radiography, projection radiography is done, but repeated many times. The repetitions produce a collection of data which is used to generate an image of the cross section of the object. That is, multiple "side views" of the object are used to generate a "cross sectional view," called a phantom. FIG. 1 illustrates, in simplified form, some basic principles of tomography.
The object 3 of FIG. 1A is conceptually divided into pixels P, as in FIG. 1B. Each ray R of radiation passing through the body is attenuated by the sequence of pixels through which it passes. A collection of parallel rays, spanning from point C to point D, produces one of the projection images.
The amount of attenuation of each ray is measured, using a detector which produces numerical output. Then, an equation is derived for each ray. A simplified example is given by FIG. 1C.
If the initial intensity of the ray is I.sub.o, and if the intensity of the ray after passing through the object is I.sub.f, then Equation (1) is obtained for FIG. 1C: EQU I.sub.f =[I.sub.o e.sup.-.alpha..sbsp.1.sup.L.sbsp.1 ][e.sup.-.alpha..sbsp.2.sup.L.sbsp.2 ][e.sup.-.alpha..sbsp.3.sup.L.sbsp.3 ](1)
Each bracketed term in Equation (1) corresponds to a position indicated in FIG. 1C.
Equation 1 results from a single ray. Since multiple rays produce each image, multiple equations are obtained for each image. Further, since numerous images are obtained, numerous sets of equations, each containing multiple equations, are obtained.
The numerous sets, of multiple equations each, are solved for the variables .alpha., three of which are found in Equation (1). Each .alpha. represents the attenuation coefficient of a pixel.
After a solution is obtained, the attenuation coefficient, .alpha., for each pixel is mapped graphically, as by using darker colors for larger coefficients, and lighter colors for smaller coefficients. The map obtained is commonly called a "phantom." Since the attenuation coefficient of each pixel can be correlated with other physical parameters associated with the pixel, such as density (ie, mass per unit volume), the mapping indicates the density pattern (or other parameter) within the phantom.
This type of tomography is called "continuous domain" tomography, because the pixels represent a continuum, in the sense that there is no vacant space between pixels.
Radiation tomography cannot be used for very small objects. One reason is that the wavelength of the radiation used limits the resolving power of the tomography, just as the wavelength of light limits the resolving power of the optical microscope. In general, the wavelength must be "small," compared with the size of the pixels.
However, if the object is sufficiently small, the pixels will be even smaller (because they must be contained within the object) and tomography cannot be used, because the pixels will be smaller than the wavelength of the radiation.
Another reason is that, in general terms, the size of each pixel P in FIG. 1B approximately equals the size of the detector (not shown) used to detect each ray R. If the object under investigation is made arbitrarily small, then the pixels become even smaller. Detectors of arbitrarily small size are typically not available.
The invention performs tomography on extremely small objects, having cross-sectional sizes, for example, in the range of 100.times.100 atoms. The invention detects the presence and absence of individual atoms at lattice sites.